All categories

1 year ago

Find the sum of the infinite geometric sequence that begins 1/12, 1/18, 1/27, …

Mathematics

1 answer:

Agata [3.3K]1 year ago

7 0

Answer:

1/4

Step-by-step explanation:

The sum of an infinite geometric series is given by the formula ...

S = a/(1 -r)

where 'a' is the first term, and r is the common ratio.

<h3>Application</h3>

Here, the first term is 1/12, and the common ratio is ...

(1/18)/(1/12) = 12/18 = 2/3

Then the sum is ...

S = (1/12)/(1 -2/3) = (1/12)/(1/3) = 3/12 = 1/4

The sum of the infinite series is 1/4.

You might be interested in

Write the algebraic expression for the difference between the squares of two numbers.

V125BC [204]

The algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is

a² - b² = (a + b)(a - b).

An algebraic expression is a combination of terms, where the terms are separated using mathematical operators like plus (+), minus (-), multiply (*), and divide (/).

The terms are combinations of numerals and variables.

Variables are represented alphanumerically, which can hold any value as per the expression they are used in.

In the question, we are asked to write the algebraic expression for the difference between the squares of two numbers.

We assume the two numbers to be a and b respectively.

Thus, we are asked to write an expression for the difference between the square of a and square of b, that is, we are asked to write an expression for a² - b².

We know that a² - b² is an identity, which can be shown as (a + b)(a - b).

Thus, the algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is a² - b² = (a + b)(a - b).

Learn more about algebraic expressions at

brainly.com/question/2241589

#SPJ4

6 0

1 year ago

PLEASEEE HELP ME WHAT IS THE ANSWER!!

blagie [28]

Answer:

Number 3 is correct.

129.19m

Step-by-step explanation:

You might be wondering how did I got 32⁰, well, that's because they are alternate angles.

Now, we're trying to find the opposite side of the triangle.

Using the laws,

we got cos32⁰=x/243.8

243.8cos32⁰=x

129.19⁰

Mark me as Brian list?

3 0

3 years ago

Which of the following lines will have a negative slope? Select all that apply

olganol [36]

Answer:

1, 5

Step-by-step explanation:

-16/4=-4

10/5=2

1/2=1/2

-1/-3=1/3

-1/4/1/2=-1/2

The negative ones are your answer.

6 0

2 years ago

Identify this conic section. x 2 + y 2 = 25 line circle ellipse parabola hyperbola

patriot [66]

Answer:

circle

Step-by-step explanation:

The equation

x² + y² = r²

Represents a circle centred at the origin with radius r

x² + y² = 25 ← is in this form and

is a circle centre (0, 0) with r = 5

7 0

3 years ago

Read 2 more answers

?<br><br>2 to the 3rd power - 5 x (6 + 4) ÷ 2<br><br>show your work

Delvig [45]

Answer:

-17

Step-by-step explanation:

$2^3$ - 5 * (6 + 4) ÷ 2

Following PEMDAS, we must focus on the parenthesis first.

$2^3$ - 5 * (6 + 4) ÷ 2

$2^3$ - 5 * (10) ÷ 2

Now we will focus on the exponent:

$2^3$ - 5 * 10 ÷ 2

8 - 5 * 10 ÷ 2

Now Multiplication/Division.

This is where you must follow the order in the equation where you see the multiplication sign first, so you multiply first.

8 - 5 * 10 ÷ 2

8 - 50 ÷ 2

Next, Divide:

8 - 50 ÷ 2

8 - 25

Subtract:

8 - 25

-17

$2^3$ - 5 * (6 + 4) ÷ 2 = -17.

4 0

3 years ago

Read 2 more answers